1Effect of Modeling Instruction on Development of Proportional Reasoning I: an empirical study of high school freshmen

Proportional reasoning is the ability to compare ratios or the ability to make statements of equality between ratios. Jean Piaget considers the ability to reason proportionally to be a primary indicator of formal operational thought, and this stage is viewed as the highest level of cognitive development. Proportional reasoning is taught primarily in mathematics courses, but student success in secondary science is highly dependent on proportional reasoning ability. The focus of this empirical study was to compare traditional math instruction to instruction that is consistent with the Modeling Method of physics instruction and findings from proportional reasoning research. Twenty-one ninth grade students in the control group received traditional math instruction while 21 students received the treatment. A proportional reasoning test instrument representing a wide variety of contextual factors was developed from items found in the literature. An independent two-tail t-test was completed with the pretest and posttest data for both groups as well as between the net gain from pretest to posttest for each group. The treatment proved to be highly significant, p<.01, indicating that the treatment developed the necessary reasoning required for greater success on the proportional reasoning instrument. The success of the treatment suggests a viable model for mathematics instruction that could lead to greater success in secondary science as well as facilitate formal operational thought